Biological design principles for robustness, performance and selective interactions with noise: The Escherichia coli heat shock response and other case studies

In this dissertation we tackle the modelling and analysis of gene regulatory networks. We specifically study the heat shock response, a cellular response by which organisms react to a sudden increase in the ambient temperature. The consequences of such an unmediated temperature increase at the cellular level is the unfolding or aggregation of cell proteins. To combat such effects, cells have evolved an intricate set of feedback and feedforward mechanisms. We present mathematical models that describe the core functionality of these mechanisms in the bacterium Escherichia coli. We illustrate how such models explain dynamic phenomena exhibited by wild type and mutant heat shock responses, corroborate experimental data and guide novel biological experiments. Furthermore, we demonstrate several design principles that appear to have shaped the feedback structure of the heat shock system. Specifically, we demonstrate the role of the various feedback strategies in achieving efficiency, robustness, stability, good transient response, and noise rejection in the presence of limited cellular energies and materials. Examined from this perspective, the heat shock model can be decomposed into functional modules that possess the characteristics of more familiar modular structures present in a typical technological control system.;Since gene regulatory networks are permanently affected by various sources of noise, we study in some detail the design principles that dictate the level of this noise and point to various strategies that lead to noise attenuation or exploitation in these systems. Specifically, we focus on noise attenuation by means of regulated protein stability, a mechanism used in the heat shock response system and ubiquitously present in a plethora of other cellular mechanisms. Although noise is traditionally associated with detrimental effects that interfere with orderly operation, we demonstrate that it can also be at the source of constructive behavior. We focus on coherence resonance as an example of noise-enhanced behavior and discuss the possibility of its occurrence in a number of simplified gene regulatory network models.;Finally, we suggest stochastic stability theory as a necessary tool to insure the absence of qualitative noise-induced change of behavior in biological systems. We illustrate this viewpoint through two relevant examples.